Table 4.

Estimates for probability of a minor epidemic or reaching an endemic level and the mean and standard deviation for duration of a minor epidemic in the CTMC SIS model (hit zero prior to reaching 30), ${\mathrm{\mathbb{P}}}_0$, Mean and STD, are computed from ${10}^6$ sample paths. These values are compared to the analytical values ${\mathrm{\mathbb{P}}}_{\text{ext}}$, μ. and σ in the birth-death process. Parameters are $\gamma =1$ and $\beta ={\mathrm{ℛ}}_0$ with initial condition $I\left(0\right)=3$.

N	$\overline{I}$	${\mathrm{ℛ}}_0$	${\mathrm{\mathbb{P}}}_0$	${\mathrm{\mathbb{P}}}_{\text{ext}}$	Mean	μ	STD	σ
2000	98	1.05	0.833	0.864	5.50	7.05	6.48	10.73
1000	48	1.05	0.840	0.864	5.60	7.05	6.58	10.73
500	24	1.05	0 0.859	0.864	5.88	7.05	7.10	10.73
2000	182	1.1	0.745	0.751	4.94	5.34	5.63	6.71
1000	91	1.1	0.753	0.751	5.08	5.34	5.87	6.71
500	45	1.1	0.772	0.751	5.36	5.34	6.30	6.71
2000	667	1.5	0.298	0.296	2.23	2.22	1.93	1.92
1000	333	1.5	0.300	0.296	2.24	2.22	1.95	1.92
500	167	1.5	0.305	0.296	2.28	2.22	2.00	1.92